Which one of these statements is true about Copernicus?

a. His model included planetary orbits that were circular.

b. He believed that Ptolemy's ideas about the shape of orbits were correct

c. His model could not account for retrograde motion of Mars.

d. His model of the universe placed the Earth, rather than the Sun, at the center.

e. His model included planetary orbits that were elliptical.

The correct statement about Copernicus is:

d. His model of the universe placed the Earth, rather than the Sun, at the center.

To determine which statement is true about Copernicus, we need to examine each statement and the information related to it.

a. His model included planetary orbits that were circular.
To verify if this statement is true, we can refer to Copernicus' model of the universe. Copernicus actually proposed that the planets orbit the Sun in circular paths (epicycles), which was a modification of the previous geocentric model devised by Ptolemy. However, Copernicus' actual model did not perfectly match the observations.

b. He believed that Ptolemy's ideas about the shape of orbits were correct.
This statement is not accurate. Copernicus disagreed with Ptolemy's geocentric model, which placed the Earth at the center of the universe. Instead, Copernicus proposed a heliocentric model, where the Sun was at the center, and the planets revolved around it.

c. His model could not account for retrograde motion of Mars.
This statement is true. While Copernicus was successful in explaining the general motion of the planets, his model did not fully account for the retrograde motion of Mars. It wasn't until later with the development of elliptical orbits by Johannes Kepler that retrograde motion was adequately explained.

d. His model of the universe placed the Earth, rather than the Sun, at the center.
This statement is not accurate. As mentioned earlier, Copernicus proposed a heliocentric model, where the Sun was at the center of the universe and the Earth and other planets orbited around it.

e. His model included planetary orbits that were elliptical.
This statement is not entirely true. While Copernicus' model included circular planetary orbits with epicycles, he did not propose elliptical orbits. It was Kepler who later discovered that the planets move in elliptical paths.

Based on the above analysis, the correct statement is:
c. His model could not account for retrograde motion of Mars.

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